Numerical analysis and implicit time stepping for high-order, fluid flow simulations on GPU architectures
Abstract/Contents
- Abstract
- High-order discontinuous finite element methods are becoming increasingly more pop- ular for simulations of vortex dominated flows over complex geometries because they are inherently less dissipative than traditional second-order finite volume methods. In particular, the Flux Reconstruction (FR) approach has gained popularity because it not only offers less dissipation but is also eminently parallelizable on multi-core processors and accelerators. An extensive amount of research has been performed for accelerated explicit methods for FR but more realistic simulations often require high aspect ratio meshes where the maximum stable time step or CFL condition is determined by the smallest cell. This can lead to significant limitations in explicit time integration. In this dissertation, eigensolution analysis is performed to study the effect of these limitations on the stability, dissipation and dispersion properties of the nodal Discontinuous Galerkin (DG) scheme via FR for advection-diffusion. It is shown that the CFL condition for advection-diffusion is stricter than that for pure-advection or pure-diffusion individually and a suitable estimate for the maximum stable time step is proposed. The CFL condition is strongly influenced by the choice of interface fluxes and, in general, the condition for a scheme using centered values is much higher than that which has one-sided values. It is also shown that schemes with centered interface values produce less error for well resolved solutions while schemes with one- sided interface values produce less error for solutions that are under-resolved. These results are verified for one- and two-dimensional advection-diffusion of an approximate Gaussian and two-dimensional Couette flow. In addition to eigensolution analysis, a multi-GPU, implicit time stepping method ivis developed, implemented and tested in order to study the feasibility of an implicit scheme on modern hardware. It is shown that a nonlinear solver can be constructed for the Direct Flux Reconstruction (DFR) method which maintains element-locality and high arithmetic intensity with minimal communication costs on modern GPU clusters. Analytical element local Jacobians for the DFR method are derived and a Kronecker product formulation is used to reduce the time complexity from O(P^(3d−1)) to O(P^(d+1)) for Euler simulations and O(P^(3d)) to O(P^(d+2)) for Navier-Stokes where P is the degree of the Lagrange basis polynomials and d is the spatial dimension. Numerical results are obtained for the inviscid bump, inviscid NACA0012 airfoil, isentropic vortex, laminar Joukowski airfoil and three-dimensional half cylinder with a Reynolds number of 1000.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Watkins, Jerry.?UNAUTHORIZED |
|---|---|
| Associated with | Stanford University, Department of Aeronautics and Astronautics. |
| Primary advisor | Jameson, Antony, 1934- |
| Thesis advisor | Jameson, Antony, 1934- |
| Thesis advisor | Alonso, Juan José, 1968- |
| Thesis advisor | Lele, Sanjiva K. (Sanjiva Keshava), 1958- |
| Advisor | Alonso, Juan José, 1968- |
| Advisor | Lele, Sanjiva K. (Sanjiva Keshava), 1958- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jerry Watkins. |
|---|---|
| Note | Submitted to the Department of Aeronautics and Astronautics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Jerry Enrique Watkins
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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